NDLI: Long-Run Accuracy of Variational Integrators in the Stochastic Context

Content Provider	Society for Industrial and Applied Mathematics (SIAM)
Author	Bou-Rabee, Nawaf Owhadi, Houman
Copyright Year	2010
Abstract	This paper presents a LieTrotter splitting for inertial Langevin equations (geometric Langevin algorithm) and analyzes its long-time statistical properties. The splitting is defined as a composition of a variational integrator with an OrnsteinUhlenbeck flow. Assuming that the exact solution and the splitting are geometrically ergodic, the paper proves the discrete invariant measure of the splitting approximates the invariant measure of inertial Langevin equations to within the accuracy of the variational integrator in representing the Hamiltonian. In particular, if the variational integrator admits no energy error, then the method samples the invariant measure of inertial Langevin equations without error. Numerical validation is provided using explicit variational integrators with first-, second-, and fourth-order accuracy.
Starting Page	278
Ending Page	297
Page Count	20
File Format	PDF
ISSN	00361429
DOI	10.1137/090758842
e-ISSN	10957170
Issue Number	1
Volume Number	48
Language	English
Publisher	Society for Industrial and Applied Mathematics
Publisher Date	2010-04-02
Access Restriction	Subscribed
Subject Keyword	Monte Carlo methods Langevin equations OrnsteinUhlenbeck equations geometric ergodicty Stochastic differential and integral equations Hamiltonian systems including symplectic integrators LieTrotter splitting variational integrators BoltzmannGibbs measure Discrete-time Markov processes on general state spaces
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Numerical Analysis Computational Mathematics

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